Method for the three dimensional measurement of a moving objects during a known movement

ABSTRACT

A 3D measurement method including; projecting a pattern sequence onto a moving object; capturing a first image sequence with a first camera and a second image sequence synchronously to the first image sequence with a second camera; determining corresponding image points in the two sequences; computing a trajectory of a potential object point from imaging parameters and from known movement data for each pair of image points that is to be checked for correspondence, The potential object point is imaged by both image points in case they correspond. Imaging object positions derived therefrom at each of the capture points in time into image planes respectively of the two cameras. Corresponding image points positions are determined as trajectories in the two cameras and the image points are compared with each other along predetermined image point trajectories and examined for correspondence; lastly performing 3D measurement of the moved object by triangulation.

RELATED APPLICATIONS

This application is a continuation of International applicationPCT/EP2017/065118 filed on Jun. 20, 2017 claiming priority from priorityfrom German patent application 10 2016 111 229.1, filed on Jun. 20,2016, and German patent application 10 2017 113 473.5, filed on Jun. 20,2017, all of which are incorporated in their entirety by this reference.

FIELD OF THE INVENTION

The invention relates to a method for three-dimensional measuring ofmoving objects performing a known movement. The method forthree-dimensional measurement of a moving object during a known relativemovement between the moving object and a measuring sensor including thesteps of projecting a pattern sequence of N patterns onto the movingobject, capturing a first image sequence of N images by a first cameraand capturing a second image sequence of N images that is synchronous tothe first image sequence by a second camera, determining correspondingimage points in the first image sequence and in the second imagesequence, computing a trajectory of a potential object point fromimaging parameters of the camera system and from known movement data foreach pair of image points of both cameras that is to be checked forcorrespondence wherein the potential object point is imaged by bothimage points in case both image points actually correspond to eachother, imaging object positions derived therefrom at each of the Ncapture points in time into image planes respectively of the first andof the second camera, the image points are compared with each otheralong predetermined image point trajectories and examined forcorrespondence in the captured image sequences, and performingthree-dimensional measurement of the moving object in a final step fromthe corresponding image points by triangulation. The positions ofcorresponding image points are determined as a first image pointtrajectory in the first camera and a second image point trajectory inthe second camera. In one embodiment moving objects are measured on aconveyor belt wherein the sensor itself is fixed relative to theconveyor belt or large objects are being measured, wherein the 3-Dsensor is continuously moved by a device, in particular a robot or acoordinate measuring machine along the object to be measured.

BACKGROUND OF THE INVENTION

Typically 3-D sensors with laser line triangulation are used for thisapplication. These sensors are insensitive with respect to relativemovements between object and sensor. However, in sensors of this typemerely a line on the object to be measured in being measured. By movingthe sensor or the object, however, many individual measurements can beperformed that can be combined into a surface measurement.

However, it is also possible to use a surface 3-D sensor with twocameras and a projector that is used to project a pattern sequence. Thisis a photogrammetry method with a structured illumination that variesover time. A measurement can therefore detect a large surface so that asurface oriented 3-D measurement can be performed in a very short time,in particular compared to methods based on laser-line triangulation.However, methods of this type are very sensitive with respect tomovements.

BRIEF SUMMARY OF THE INVENTION

Thus, it is an essential prerequisite for this method that each imagepoint forms the same object point during the entire detection. Neitherthe measured object nor the sensor may move relative to each otherduring the measurement. There have been attempts to compensate movementsduring capturing a sample image sequence. One of these approaches isdescribed in Harendt, B. Groebe, M.; Schaffer, M. & Kowarschik, R. “3Dshape measurement of static and moving objects with adaptivespatiotemporal correlation applied Optics”, 2014, 53, 7507-7515 or inBreitbarth, A. Kuehmstedt, P.; Notni, G. & Denzler, J. “Motioncompensation for three-dimensional measurements of macroscopic objectsusing fringe projection” DGaO Proceedings, 2012, 113.

These known approaches use an iteration method. Initially a coarsenon-movement sensitive measurement is performed. The results of themeasurement are subsequently used to compensate the movement and toperform a point association using time based features.

A disadvantage of these approaches is the iteration method whichstrongly limits precision of the 3-D measurement.

Thus, it is an object of the invention to perform surface oriented 3-Dcapturing that is not sensitive relative to movements and on the otherhand side to overcome the disadvantages of the iteration detection.

The object is achieved by a method for three-dimensional measurement ofa moving object during a known relative movement between the movingobject and a measuring sensor including the steps of projecting apattern sequence of N patterns onto the moving object, capturing a firstimage sequence of N images by a first camera and capturing a secondimage sequence of N images that is synchronous to the first imagesequence by a second camera, determining corresponding image points inthe first image sequence and in the second image sequence, computing atrajectory of a potential object point from imaging parameters of thecamera system and from known movement data for each pair of image pointsof both cameras that is to be checked for correspondence wherein thepotential object point is imaged by both image points in case both imagepoints actually correspond to each other, imaging object positionsderived therefrom at each of the N capture points in time into imageplanes respectively of the first and of the second camera, the imagepoints are compared with each other along predetermined image pointtrajectories and examined for correspondence in the captured imagesequences, and performing three-dimensional measurement of the movingobject in a final step from the corresponding image points bytriangulation. The positions of corresponding image points aredetermined as a first image point trajectory in the first camera and asecond image point trajectory in the second camera.

It is a prerequisite for this solution that information regarding themovement of the measured object relative to the sensor is known, e.g.when measuring an object on a conveyor belt or when measuring a staticobject with a sensor that is moved over the measured object by a robot.

The method for three-dimensional measurement of the moving object isperformed with the following method steps when movement data is known.

A pattern sequence of N patterns is projected onto the moving object,

Thereafter capturing of a first image sequence of N images is performedby a first camera and capturing of a second image sequence of N imagesthat is synchronous to the first image sequence is performed by a secondcamera.

Thereafter determining corresponding image points in the first imagesequence and in the second image sequence is performed whereintrajectories of potential object points are computed from the knownmovement data and object positions derived therefrom are projected ontoimage planes respectively of the first and of the second camera, whereinthe positions of corresponding image points are determined in advance asa first image point trajectory in the first camera and a second imagepoint trajectory in the second camera.

The image points are compared with each other along predetermined imagepoint trajectories and examined for correspondence. Thethree-dimensional measurement of the moving object is performed in afinal step from the corresponding image points by triangulation.

When comparing the image points along the predetermined first and secondimage point trajectories a first gray scale sequence is determined in anembodiment in the first camera and a second gray scale sequence isdetermined in the second camera and a similarity of the first and thesecond gray scale sequence is determined.

Depending on the embodiment a similarity of gray scale sequences isdetermined by performing a standardized cross correlation, a sum ofabsolute differences and/or a phase evaluation.

In one embodiment a sequence of static patterns is used as a projectedpattern sequence.

The projected pattern sequence can be, e.g., a sequence of phase shiftedsine-shaped stripe patterns.

A static pattern can also be used as a projected pattern sequencewherein a projection of the static pattern on the measured object isvaried at will with respect to its position and/or shape.

BRIEF DESCRIPTION OF THE DRAWINGS

The method will be subsequently described based on embodiments withreference to drawing figures, wherein:

FIG. 1 illustrates a geometric representation of the method;

FIGS. 2 and 3 illustrate exemplary image point trajectories as afunction of time; and

FIG. 4 illustrates a three-dimensional measurement system capable ofimplementing the method according the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The method according to the invention is based on the following idea:

Under the presumption that it is known at which location an object pointis at a certain point in time (position vector) and how the object pointmoves from there (displacement vector), it can be predetermined how acorresponding image point of the object point will move in a camera of acalibrated camera system. This information regarding the movement can beused in that associating corresponding image points is not done bycomparing time-based gray scale sequences of fixed pixels with eachother, but in that time-based gray scale sequences are compared witheach other along the trajectories of the image points of an object pointin the image planes of both cameras.

When there is a pure translatoric movement, a movement of all objectpoints, thus their displacement vector, is identical. On a conveyor beltthis movement can be determined in that the movement direction of theconveyor belt is calibrated. However, a movement of an image point inthe camera is not predeterminable when a distance of the correspondingobject point is unknown, namely the further the object point is remotefrom an image detection device, the smaller the displacement of theimage point in the image plane. In addition to the movement information,information regarding a position of the object point is required inorder to compensate a movement of the object point.

In principle it is possible to solve this problem by iteration and byinitial coarse determination of the position vectors of all objectpoints with a non-movement sensitive method and to estimate theirtrajectories in the images of both sensor cameras. This, however, isvery imprecise.

The method according to the invention works without this iterativeprocedure. It rather uses the fact that comparing the gray scalesequences of two image points with one another includes actuallyimplicitly checking whether the two image points depict the same objectpoint. Thus it is checked implicitly whether the possible object pointis at a predetermined location in space, namely at the location wherethe viewing beams of both image points intersect. When the viewing beamsare skewed, this corresponds to the location that has the smallestdistance from both viewing beams. When comparing image points thepresumption is checked whether an object point is at the correspondingposition in space.

Comparing two image points and presuming that the respective objectpoint is actually at a position where the viewing beams of the two imagepoints intersect at least approximately, it can be predetermined basedon knowledge of the movement of the measured object how the respectiveimage points in both cameras change when the object point moves.Initially the trajectory of the object point is construed from theposition vector of the object point and from the movement data. Thetrajectory is then projected back into the image planes of both camerasusing the calibration data of the camera system. Thus, it is computedfor each capture point in time of the camera where the potential objectpoint would be located at this point in time and the simulated 3-Dposition is introduced into the image planes of both cameras, this meansprojected.

In order to check similarity of two image points the invention does notcompare the time based gray scales at stationary image points in theimage plane according to FIG. 2 like for static objects. Rather, grayscales along the time based image point trajectories according to FIGS.1 and 3 are compared.

This method is certainly not limited to translatoric movements. Anymovement of rigid measured objects, thus also rotating movements, can becompensated if the corresponding movement data is known. Theoreticallyalso deformations of the object can be compensated if correspondingmovement data can be obtained.

The method is performed as follows:

Initially information regarding the movement of the measured object ispredetermined externally. For this purpose the movement direction of aconveyor belt can be calibrated in advance. The current movementvelocity and/or position of the conveyor belt can be determined by anencoder of the conveyor belt or by another position measuring device.

Next, a sample image sequence of N images is projected and captured bytwo synchronous cameras. Thus, each camera captures an image sequencerespectively with N images of the measured object with patternsprojected onto it. During the capture the measured object moves with aknown velocity.

The sample image sequence of N images can include for example of phaseshifted sine shaped stripe patterns and/or of random patterns, e.g.,band limited statistic patterns. The pattern sequence can also begenerated in that an individual pattern is projected onto the measuredobject and changed there in any way with respect to position and/orshape, thus, e.g. a static pattern that is continuously moved on acircular path over the measured object. The latter example shows thatthe term “sample image sequence” must not be interpreted in a narrowmanner so that a sample image sequence always has to consist of adiscrete sequence of N different image patterns that are projected ontothe measured object.

In the captured image sequences corresponding image points, this meansimage points that image the same object point, are being searched for bysearching for each pixel of the first camera a pixel of the secondcamera which has the highest similarity with the first pixel.

The similarity of two pixels from two cameras is determined, e.g., asfollows and reference is made to the illustration of FIG. 1:

Initially it is determined by triangulation where a corresponding objectpoint 5 would be located when the two pixels 9 and 16 would actuallyimage the same object point.

A trajectory 19 of the potential object point 5 is reconstrued in threedimensions from the known movement information of the measured object(e.g., 17 and 18) so that a potential position of the moved object pointis known for each point in time of image capture t=1, 2, 3 . . . , N ofthe captured sample image sequence 5, 6, 7, . . . , 8, wherein thepotential position of the moved object point is: P(t=1), P(t=2), P(t=3),. . . , P(t=N). This is emphasized by the reference numerals 5, 6, 7, .. . 8.

The position of the object point that is known at each point in time ofcapturing the sample image sequence is respectively projected back intothe image planes 1 and 2 of the cameras with the projection centers 3and 4. In the illustrated embodiment the aperture camera model isoptically used, as a matter of principle, however, also other cameramodels are possible.

These projections yield trajectories 21 and 20 of the image points ofthe potential object point in the camera images. Thus, the position ofthe image points that would image the potential object point is knownfor both cameras and each point in time t of image capture. Inparticular, these are the image points B1(t=1), B1(t=2), B1(t=3) . . . ,B1(t=N), thus indicated by the reference numerals 9, 10, 11, 12 forcamera 1 and the image points B2(t=1), B2(t=2), B2(t=3), . . . ,B2(t=N), thus indicated by the reference numerals 16, 15, 14 and 13 forcamera 2.

Next, gray scale sequences along both image point trajectories 21, 20are extracted, thus the gray scale sequence G1(t=1), G1(t=2), G1(t=3), .. . , G1(t=N), for camera 1 and the gray scale sequence G2(t=1),G2(t=2), G2(t=3), . . . , G2(t=N) for camera 2. For example G2(t=3)designates the gray scale value at the image point B2(t=3) in camera 2in the third image of the capture sequence.

In FIG. 3 image point trajectories 21 and 20 are presented in arepresentation that plots location over time. With increasing capturetime different image points are excited and a location of the excitationmoves over the capture field of the respective camera. For comparisonFIG. 2 shows a trajectory with location plotted over time where theimage points respectively remain constant in space as the capture pointin time progresses as it is the case for static measured objects. Bothtrajectories of FIG. 2 and FIG. 3 are associated with respective grayscale sequences and the two trajectories can be processed with the sameprocedure.

Since the image points are typically arranged at sub pixel locations thecorresponding intensity values can also be interpolated from theintensity values of the adjacent pixels.

Next the similarity of the gray scale sequences is determined. As ameasure for the similarity a standardized cross correlation can be used.Other similarity measures like e.g. the sum of absolute differences or aphase evaluation, however, are possible as well. A selection of thedegree of similarity depends from the type of the projected patterns.For static patterns a standardized cross correlation may be used, forphase shifted sine shaped stripe patterns a phase evaluation isparticularly advantageous.

An image point in camera 2 is associated with an image point in camera 1as a corresponding image point when it has the highest level ofsimilarity of all image points in camera 2 with respect to the imagepoint in camera 1. Optionally the search portion in camera 1 can belimited to an optical or geometrically suitable detail, e.g. to a socalled epipolar line.

When required point correspondences with maximum similarity can also bedetermined down to sub pixels. It is apparent that the described methodfor evaluating the similarity of two image points can also be used forsub pixel locations.

3D points are reconstrued from corresponding image points in a knownmanner by triangulation.

Depending at which point in time t=1, 2, 3, or N the measured objectshall be reconstrued (B1(t=1), (B2(t=1), (B2(t=2), (B1(t=3), (B2(t=3),(B1(t=N), (B2(t=N), thus emphasized by the reference numerals (9, 16),(10, 15), (11, 14), . . . or (12, 13) have to be used as correspondingimage point pairs during the triangulation.

The described method is not limited to translatoric movements. Rotationsor combination of linear movement and rotation can be compensated aswell.

The complexity of the image point trajectories 21 and 20 is a functionof the complexity of the movement. For any linear movement and rotation,however position and shape of the trajectories are a function of therespective image point pair 9, 16. In case of a straight linearmovement, e.g. for measuring objects on a conveyor belt the image pointtrajectories simplify into straight lines. This is the case inparticular for non-distorting cameras which correspond to the aperturecamera model.

Theoretically even any movements can be compensated, thus alsodeformations in case corresponding movement information can bedetermined and is provided. During linear movement and rotation this canbe accomplished easily. For example when attaching a sensor at a robotand calibrating position and orientation of the sensor relative to therobot flange, in particular during a so called hand-eye calibration, therobot can signal an actual position and orientation of the sensor in therobot coordinate system at any point in time. From this information atrajectory in a moved sensor coordinate system can be determined for anobject point that is unmoved with respect to the robot coordinatesystem.

The movement of a movable 3D-sensor relative to a static measured objectcan also be determined synchronously with capturing the measured objectby the 3D sensor using additional sensors, not necessarily opticalsensors. For example, markers can be attached on the primary 3D-sensorwherein a movement of the markers can be tracked with additional camerasand the position change of the 3D sensor relative to the static measuredobject is determined from the movement of the markers. This movementinformation can then be compensated by the described method duringthree-dimensional reconstruction of the measured object.

The relative movement of the 3D-sensor and the measured object can alsobe determined by the 3D-sensor itself. For example, statistic patternscan be used for pattern projection according to the described method andeach synchronously captured stereo image pair (t=1, t=2, t=N) can beadditionally separately processed by non-movement sensitive but coarsespatial correlation. As a result a rather coarse but tightly orimprecisely reconstrued point cloud of the measured object is achievedat each point in time of capture. t=1, t=2, t=N. However, when the pointclouds of sequential points in time of capture t=1 and t=i+1 (i=1, 2,N−1) are brought into coincidence using an ICP method (iterative closestpoint) information is obtained regarding the relative movement, thismeans the linear movement and rotation of the measured object betweent=i and t=i+1, and thus when this step is performed for i=1 throughi=N−1 over the entire trajectory of the measured object from t=1 to t=N.This movement information can then be compensated in the context of thedescribed method during three-dimensional construction of the measuredobject.

In analogy to the previously described approach for obtaining movementinformation the movement of the measured object relative to the 3Dsensor can also be determined by an additional sensor that is fixedrelative to the 3D sensor and calibrated relative to the 3D sensor. Thisadditional sensor detects the measured object synchronously to theactual 3D-sensor and provides a coarse point cloud of the measuredobject for each point in time of capture t=1, t=2, t=N. Movementinformation can be obtained from the coarse point clouds in thepreviously described manner using the ICP method. It is an advantage ofthe additional sensor that it can be configured especially for the taskof delivering precise movement information. This precise movementinformation can be based on non-movement sensitive methods which provideeither few precise measuring points or many non-precise measuring pointsof the analyzed measuring object depending on which method provides thebest movement information.

FIG. 4 illustrates a three-dimensional measurement system 40 capable ofimplementing the method according the present invention. Thethree-dimensional measurement system 40 includes a first camera 42, asecond camera 44, a projector for projecting patterns 46, and aprocessor 48 such as a computer. The three-dimensional measurementsystem 40 uses the processor 48 to take the inputs from the first camera42 and the second camera 44, in conjunction with the operation of theprojector 46, to perform the three-dimensional measurement of a movingobject according to the method of the invention.

The method according to the invention was described based onembodiments. A person skilled in the art will be able to combine thefeatures of the invention into additional embodiments.

The invention claimed is:
 1. A method for three-dimensional measurementof a moving object during a known relative movement between the movingobject and a measuring sensor, the method comprising the steps:projecting a pattern sequence of N patterns onto the moving object;capturing a first image sequence of N images by a first camera andcapturing a second image sequence of N images that is synchronous to thefirst image sequence by a second camera; determining corresponding imagepoints in the first image sequence and in the second image sequence;computing a trajectory of a potential object point from imagingparameters of both cameras and from known movement data for each pair ofimage points of both cameras that is to be checked for correspondence,wherein the potential object point is imaged by both image points incase both image points actually correspond to each other; imaging objectpositions derived therefrom at each of N capture points in time intoimage planes respectively of the first camera and of the second camera,wherein positions of the corresponding image points are determined as afirst image point trajectory in the first camera and a second imagepoint trajectory in the second camera and the image points are comparedwith each other along predetermined image point trajectories andexamined for correspondence in the captured first and second imagesequences; performing three-dimensional measurement of the moving objectin a final step from the corresponding image points by triangulation. 2.The method according to claim 1, further comprising the step: comparingthe image points along the predetermined first and second image pointtrajectories by determining a first gray scale sequence from thecaptured first image sequence of the first camera and a second grayscale sequence from the captured second image sequence of the secondcamera and determining a similarity of the first gray scale sequence andthe second gray scale sequence.
 3. The method according to claim 2,wherein determining the similarity of the first gray scale sequence andthe second gray scale sequence includes using a standardized crosscorrelation, a sum of absolute differences, a phase processing or acomparable known measure of similarity for determining a correlation ofgray scale sequences.
 4. The method according to claim 1, wherein asequence of static patterns is used as the projected sequence of Npatterns.
 5. The method according to claim 1, wherein a sequence ofphase shifted sine shaped stripe patterns is used as the projectedsequence of N patterns.
 6. The method according to claim 1, wherein astatic pattern is used as the projected sequence of N patterns, andwherein a projection of the static pattern onto the moving object isadjusted at will with respect to position or shape.
 7. An apparatus forthree-dimensional measurement of a moving object during a known relativemovement between the moving object and a measuring sensor, the apparatuscomprising a processor in communication with memory, the processor beingconfigured to execute instructions stored in the memory that cause theprocessor to perform a method comprising the steps: causing a projectorto project a pattern sequence of N patterns onto the moving object;causing a first camera to capture a first image sequence of N images anda second camera to capture a second image sequence of N images that issynchronous to the first image sequence; determining corresponding imagepoints in the first image sequence and in the second image sequence;computing a trajectory of a potential object point from imagingparameters of both cameras and from known movement data for each pair ofimage points of both cameras that is to be checked for correspondence,wherein the potential object point is imaged by both image points incase both image points actually correspond to each other; imaging objectpositions derived therefrom at each of N capture points in time intoimage planes respectively of the first camera and of the second camera,wherein positions of the corresponding image points are determined as afirst image point trajectory in the first camera and a second imagepoint trajectory in the second camera and the image points are comparedwith each other along predetermined image point trajectories andexamined for correspondence in the captured first and second imagesequences; performing three-dimensional measurement of the moving objectin a final step from the corresponding image points by triangulation. 8.The apparatus according to claim 7, further comprising the step:comparing the image points along the predetermined first and secondimage point trajectories by determining a first gray scale sequence fromthe captured first image sequence of the first camera and a second grayscale sequence from the captured second image sequence of the secondcamera and determining a similarity of the first gray scale sequence andthe second gray scale sequence.
 9. The apparatus according to claim 8,wherein determining the similarity of the first gray scale sequence andthe second gray scale sequence includes using a standardized crosscorrelation, a sum of absolute differences, a phase processing or acomparable known measure of similarity for determining a correlation ofgray scale sequences.
 10. The apparatus according to claim 7, wherein asequence of static patterns is used as the projected sequence of Npatterns.
 11. The apparatus according to claim 7, wherein a sequence ofphase shifted sine shaped stripe patterns is used as the projectedsequence of N patterns.
 12. The apparatus according to claim 7, whereina static pattern is used as the projected sequence of N patterns, andwherein a projection of the static pattern onto the moving object isadjusted at will with respect to position or shape.
 13. A non-transitorycomputer-readable storage medium storing instructions forthree-dimensional measurement of a moving object during a known relativemovement between the moving object and a measuring sensor that, whenexecuted by a processor, cause the processor to perform a methodcomprising the steps: projecting a pattern sequence of N patterns ontothe moving object; capturing a first image sequence of N images by afirst camera and capturing a second image sequence of N images that issynchronous to the first image sequence by a second camera; determiningcorresponding image points in the first image sequence and in the secondimage sequence; computing a trajectory of a potential object point fromimaging parameters of both cameras and from known movement data for eachpair of image points of both cameras that is to be checked forcorrespondence, wherein the potential object point is imaged by bothimage points in case both image points actually correspond to eachother; imaging object positions derived therefrom at each of N capturepoints in time into image planes respectively of the first camera and ofthe second camera, wherein positions of the corresponding image pointsare determined as a first image point trajectory in the first camera anda second image point trajectory in the second camera and the imagepoints are compared with each other along predetermined image pointtrajectories and examined for correspondence in the captured first andsecond image sequences; performing three-dimensional measurement of themoving object in a final step from the corresponding image points bytriangulation.
 14. The non-transitory computer-readable storage mediumaccording to claim 13, further comprising the step: comparing the imagepoints along the predetermined first and second image point trajectoriesby determining a first gray scale sequence from the captured first imagesequence of the first camera and a second gray scale sequence from thecaptured second image sequence of the second camera and determining asimilarity of the first gray scale sequence and the second gray scalesequence.
 15. The non-transitory computer-readable storage mediumaccording to claim 14, wherein determining the similarity of the firstgray scale sequence and the second gray scale sequence includes using astandardized cross correlation, a sum of absolute differences, a phaseprocessing or a comparable known measure of similarity for determining acorrelation of gray scale sequences.
 16. The non-transitorycomputer-readable storage medium according to claim 13, wherein asequence of static patterns is used as the projected sequence of Npatterns.
 17. The non-transitory computer-readable storage mediumaccording to claim 13, wherein a sequence of phase shifted sine shapedstripe patterns is used as the projected sequence of N patterns.
 18. Thenon-transitory computer-readable storage medium according to claim 13,wherein a static pattern is used as the projected sequence of Npatterns, and wherein a projection of the static pattern onto the movingobject is adjusted at will with respect to position or shape.